A search for potential point sources of very high energy gamma rays has been carried out on the data taken simultaneously by the HEGRA AIROBICC and Scintillator arrays from August 1994 to March 2000. The list of sought sources includes supernova remnants, pulsars, AGNs and binary systems. The energy threshold is around 15 TeV. For the Crab Nebula, a modest excess of 2.5 standard deviations above the cosmic ray background has been observed. Flux upper limits (at 90% c.l.) of around 1.3 times the flux of the Crab Nebula are obtained, on average, for the candidate sources. A different search procedure has been used for an all-sky search which yields absolute flux upper limits between 4 and 9 crabs depending on declination, in the band from 0 to 60 degrees.